Method and device using productivity index in drill guidance for drilling slanted water injection wells

ABSTRACT

A drill guidance device, a method to control a trajectory of a drill, and a non-transitory computer readable medium that determine the corrected drill angle and send an output signal to a drill controller configured to control an angle of a drill. The corrected drill angle is determined by at least one of a slant angle data and a formation property data received from a sensor device. The drill guidance device, the method to control a trajectory of a drill, and the non-transitory computer readable medium can be implemented in a measuring while drilling model to provide live guidance during a drilling operation or a predictive model to plan prior to the start of a drilling operation. The corrected drill angle is acted upon by a drill controller to maximize the productivity of an oil reservoir.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.62/155,184 filed Apr. 30, 2015.

BACKGROUND OF THE INVENTION

Technical Field

The present invention relates to a device, method and non-transitorycomputer readable media to guide a drill during well drilling, and toguide a drill during well drilling for water injection well used toimprove the production of hydrocarbons from an oil reservoir.

Description of the Related Art

The “background” description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent it is described in thisbackground section, as well as aspects of the description which may nototherwise qualify as prior art at the time of filing, are neitherexpressly or impliedly admitted as prior art against the presentinvention.

The inflow performance relationship (IPR) represents a crucial factor inestimating and evaluating the reservoir behavior. It is of importance toproduction and reservoir engineers. The IPR is synonymous with aquantity called the productivity index (PI), or the injectivity index(II) for injection wells. It is a relationship between the reservoirflow/injection rate and the flowing/injection bottom-hole pressure(PWF/PWJ). For water supply and water injection wells, it is a functionof many reservoir parameters like reservoir thickness, permeability,drainage radius, and skin as well as well geometry. For every reservoirwith different rock and fluid properties and different types of wells,the PI is calculated according to distinct process using a particularequation. Most of the published work and methods were developed forvertical, single horizontal and multilateral wells. Slanted models areuncommon for hydrocarbon wells. The most widely used models forcalculating PI for slanted wells express the well deviation effect intoa pseudo-skin of a vertical well's IPR.

Reservoirs put on production will experience a decline in its pressurewith time unless there is a strong pressure support from an aquifer or agas cap. In absence of this natural support, artificial pressuremaintenance is needed to boost and preserve the reservoir energy and tokeep the pressure above the bubble point to prolong profitability of thereservoir. Water flooding is the most common and successful operation toachieve this goal. Generally, water flooding operations involveinjecting huge amounts of water into the reservoir. This amount of watercan be supplied form a nearby water formation or be treated sea water;so some wells are drilled into water-producing formation and are used aswater supply for hydrocarbon production.

In oil fields, oil and water wells are drilled in many ways in order toreach a pay zone. These wells can be vertical, directional, horizontalor a combination of any of these geometries. Some conditions may dictatethe path of the well like lithology, engineering aspects, economics,location etc. For example, in offshore rigs it is favorable to drillwells with an angle (slanted), highly deviated or horizontally to drainthe reservoir. Near populated areas, wells are sidetracked from adistance to reach the reservoir. In some cases drilling a well may notgo as planned and the well penetrates the reservoir with an angle fromone or more bedding planes. Generally, slanted wells are those wellswith an angle between 15° to 60°, whereas wells with an angle greaterthan 60° are considered highly-deviated. Slanted wells' most importantadvantage is to increase the contact area with the reservoir in order toachieve higher productivity/injectivity. Though, the cost of drillingslanted or horizontal well is much higher than drilling a wellvertically.

For a vertical well producing from a single-oil reservoir, theproductivity index (PI) can be given from Darcy's law as:

$\begin{matrix}{{PI} = {\frac{q_{o}}{P_{e} - P_{wf}} = \frac{kh}{141.2\mspace{14mu} B_{o}{\mu_{o}\left\lbrack {{\ln\left( \frac{r_{e}}{r_{w}} \right)} + s} \right\rbrack}}}} & (1)\end{matrix}$

Where PI is Productivity Index (STB/Day/PSI), q_(o) is Oil Production(STB/D), P_(e) is Reservoir Pressure (PSI), P_(wf) is Flowing BottomHole Pressure (PSI), k is permeability (MD), h is Reservoir Thickness(FT), B_(o) is Oil formation Volume Factor (RB/STB), μ_(o) is OilViscosity (CP), r_(e) is Drainage Radius (FT), r_(w) is Wellbore Radius(FT), s is Skin Factor (Dimensionless).

$\begin{matrix}{{II} = {\frac{q_{w}}{P_{wfi} - P_{e}} = \frac{kh}{141.2\mspace{14mu} B_{w}{\mu_{w}\left\lbrack {{\ln\left( \frac{r_{e}}{r_{w}} \right)} + s} \right\rbrack}}}} & (2)\end{matrix}$

For Water Injection, the injectivity index (II) can be determined as:Where II is Injectivity Index (STB/Day/PSI), q_(w) is Water Injection(STB/D), P_(e) is Reservoir Pressure (PSI), P_(wfi) is Bottom HoleInjection Pressure (PSI), B_(w) is Water formation Volume Factor(RB/STB), and μ_(w) is Water Viscosity (CP).

The right-hand side of equations (1) and (2) is identical for a watersupplier and a water injector, because in both cases the fluid is water.As for slanted and highly-deviated wells, Choi et al. (2008) disclosedthat “no analytical correlations identified for slanted well geometry;instead, three correlations for deviation skin were applied to combinewith any correlation made for the vertical well to calculate PI forslanted wells”. See Choi, S. K., Ouyang, L. B. and Huang, W. S., “AComprehensive Comparative Study on Analytical PI/IPR Correlations”, SPE116580 presented at the 2008 SPE Annual Technical Conference andExhibition of the Society of Petroleum Engineering held in Denver,Colo., USA, 21-24 Sep. 2008, incorporated herein by reference in itsentirety. Cinco et al. (1975) proposed a simple correlation for slantedskin based on the study of unsteady state flow of a slightlycompressible fluid. See Cinco, H., Miller, F. G., and Ramey, H. J.,“Unsteady-State Pressure Distribution Created By a Directionally DrilledWell”, JPT, p 1392-1400, November, 1975, incorporated herein byreference in its entirety. This correlation is valid for well deviationangles between 0 to 75°:

$\begin{matrix}{{s_{\theta} = {{- \left( \frac{\theta_{w}^{\prime}}{41} \right)^{2.06}} - {\left( \frac{\theta_{w}^{\prime}}{56} \right)^{1.865}{\log_{10}\left( \frac{h_{D}}{100} \right)}}}}{Where}{{\theta_{w}^{\prime} = {\tan^{- 1}\left( {\sqrt{\frac{k_{v}}{k_{h}}}{\tan(\theta)}} \right)}},{h_{D} = {\frac{h}{r_{w}}\sqrt{\frac{k_{h}}{k_{v}}}}}}} & (3)\end{matrix}$k_(v) is the Vertical Permeability (MD), k_(h) is HorizontalPermeability (MD), θ is the Deviation Angle (Degree), h is the ReservoirThickness (FT).

Besson (1986) proposed another slanted well skin correlation from theresults of a semi-analytical simulator. See Besson, J., “Performance ofSlanted and Horizontal Wells on an Anisotropic Medium”, SPE 20965,October 1986, incorporated herein by reference in its entirety. Forisotropic reservoir and slant angles between 0° to 90°:

$\begin{matrix}{s_{\theta} = {{\ln\left( \frac{4r_{w}}{L} \right)} + {\frac{h}{L}{\ln\left( \frac{\sqrt{Lh}}{4r_{w\;}} \right)}}}} & (4)\end{matrix}$and for anisotropic reservoir:

$\begin{matrix}{{s_{\theta} = {{\ln\left( {\frac{4r_{w}}{L}\frac{1}{\propto \gamma}} \right)} + {\frac{h}{\gamma\; L}{\ln\left( {\frac{\sqrt{Lh}}{4r_{w}}\frac{2\alpha\sqrt{\gamma}}{1 + {1/\gamma}}} \right)}}}}{where}{{\alpha = \sqrt{k_{h}/k_{v}}},{\gamma = \sqrt{\frac{1}{\alpha^{2}} + {\frac{h^{2}}{L^{2}}\left( {1 - \frac{1}{\alpha^{2}}} \right)}}}}} & (5)\end{matrix}$and L is the well length.Rogers and Economides (1996) presented an expression for the pseudo-skinas:

$\begin{matrix}{s_{\theta} = {{{- 1.64}\;\frac{\sin\;\theta^{1.77}h_{D}^{0.184}}{I_{ani}^{0.821}}\mspace{14mu}{for}\mspace{14mu} I_{ani}} < 1}} & (6) \\{{s_{\theta} = {{{- 2.48}\;\frac{\sin\;\theta^{5.87}h_{D}^{0.152}}{I_{ani}^{0.964}}\mspace{14mu}{for}\mspace{14mu} I_{ani}} > 1}}{Where}{{I_{ani} = \sqrt{\frac{k_{h}}{k_{v}}}},{k_{h} = \sqrt{k_{x}k_{y}}},{h_{D} = \frac{h}{r_{w\;}}}}} & (7)\end{matrix}$See Roger, E., and Economides, M., “The Skin due to Slant of deviatedWells in Permeability-Anisotropic Reservoirs”, SPE 37068, November 1996,incorporated herein by reference in its entirety. Slanted wells producemore fluid from the reservoir than vertical wells do because of theincreased area open to flow. Similarly for the injection wells, theyachieve higher injectivity and perform better in compared to verticalwells. Cinco, Besson and Economides expressed the effect of well slantinto the form of pseudo-skin.

The present disclosure is concerned with the performance of wells thatoperate as slanted and highly-deviated water supply and water injectionwells.

BRIEF SUMMARY OF THE INVENTION

According to a first aspect the present disclosure includes a drillguidance device comprising circuitry that is configured to determine aslant angle of a drill based on directional sensor data received fromone or more sensor devices, determine one or more formation propertiesbased on formation sensor data received from the one or more sensordevices, calculate a corrected drill angle based on the slant angle andthe formation properties, and output the corrected drill angle to adrill controller configured to control an angle of trajectory of thedrill.

In some implementations of the drill guidance device, the circuitry maybe further configured to determine the slant angle based on thedirectional sensor data received from at least one of an accelerometerand a magnetometer.

In some implementations of the drill guidance device, one of theformation properties is a formation permeability.

In some implementations of the drill guidance device, the formationpermeability can be based on the formation sensor data received from aporosity sensor.

In some implementations of the drill guidance device, one of theformation properties is a formation thickness.

In some implementations of the drill guidance device, the formationthickness may be based on the formation sensor data received from aresistivity sensor or a conductivity sensor.

In some implementations of the drill guidance device, the circuitry maybe further configured for manual guidance of the drill.

In some implementations of the drill guidance device, the circuitry maybe further configured to determine at least one of the slant angleand/or the formation property to increment, determine a firstproductivity index from the slant angle and/or the formation property,determine a second productivity index from an incremented slant angleand/or an incremented formation property, and determine the correcteddrill angle corresponding to the greater of the first productivity indexand the second productivity index.

In some implementations of the drill guidance device, the firstproductivity index or the second productivity index (J) is defined by:

${J = {\frac{kh}{141.2\left\lbrack {\ln\left( \frac{r_{e}}{r_{w}} \right)} \right\rbrack} + {0.0025\left\lbrack {h^{0.65}{k^{0.52}\left( {\tan\;\frac{\theta}{4}} \right)}^{1.22}} \right\rbrack}^{1.9267}}},$in which r_(e) is a drainage radius or an external boundary radius andr_(w) is a wellbore radius, slant angle is θ, formation permeability isk, and formation thickness is h.

In some implementations of the drill guidance device, the circuitry isfurther configured to recursively calculate the second productivityindex when the second productivity index is less than the firstproductivity index.

In some implementations of the drill guidance device, the circuitry isfurther configured to determine the corrected drill angle based on aproductivity index predictively calculated by accessing historical datafrom memory.

In some implementations of the drill guidance device, the correcteddrill angle is based on a continuously calculated productivity index ina measuring while drilling operation.

According to another aspect, the present disclosure includes a method tocontrol a trajectory of a drill that comprises determining a slant angleof a drill based on directional sensor data received from one or moresensor devices, determining one or more formation properties based onformation sensor data received from the one or more sensor devices,calculating a corrected drill angle based on the slant angle and theformation properties, and outputting the corrected drill angle to adrill controller configured to control an angle of trajectory of thedrill.

In some implementations of the method, the corrected drill angle isbased on a productivity index (J) calculated as a function of the slantangle and at least one of a formation permeability and a formationthickness.

In some implementations of the method, the productivity index (J) iscalculated based on the function:

${J = {\frac{kh}{141.2\left\lbrack {\ln\left( \frac{r_{e}}{r_{w}} \right)} \right\rbrack} + {0.0025\left\lbrack {h^{0.65}{k^{0.52}\left( {\tan\;\frac{\theta}{4}} \right)}^{1.22}} \right\rbrack}^{1.9267}}},$in which r_(e) is a drainage radius or an external boundary radius andr_(w) is a wellbore radius slant angle is θ, formation permeability isk, and formation thickness is h.

In some implementations of the method, the productivity index isrecursively calculated.

In some implementations of the method, calculating the corrected drillangle further includes incrementing at least one of the slant angleand/or the formation properties to form a second slant angle and/or asecond formation property. As used herein the descriptor “second” whendescribing slant angle, formation permeability, or formation thickness,may be used interchangeably with the word “incremented.”

In some implementations of the method, the method can also includecalculating a first productivity index with the slant angle and/or theformation property and a second productivity index with the second slantangle and/or the second formation property and determining when thesecond productivity index is greater than the first productivity index.

In some implementations, the method also includes determining thecorrected drill angle associated with the second formation propertyand/or the second slant angle when the second productivity index isgreater than the first productivity index.

According to an aspect, a non-transitory computer readable medium havinginstructions stored therein that, when executed by one or moreprocessors, cause the one or more processors to perform a method ofcontrolling a trajectory of a drill by a drilling guidance device, themethod comprises determining a slant angle of a drill based ondirectional sensor data received from one or more sensor devices,determining one or more formation properties based on formation sensordata received from the one or more sensor devices, controlling an angleof trajectory of the drill based on a corrected drill angle calculatedrecursively based on the slant angle and the formation properties, andproducing an output of the corrected drill angle to a drill controller.

The foregoing paragraphs have been provided by way of generalintroduction, and are not intended to limit the scope of the followingclaims. The described implementations, together with further advantages,will be best understood by reference to the following detaileddescription taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the disclosure and many of the attendantadvantages thereof will be readily obtained as the same becomes betterunderstood by reference to the following detailed description whenconsidered in connection with the accompanying drawings, wherein:

FIG. 1 is an exemplary graph of a model of productivity index for avertical well and slanted well;

FIG. 2 is an exemplary plot of a model of dJ versus slant angle;

FIG. 3 is an exemplary plot of points between dJ and MP and the equationfor the best-fit line representing those points;

FIG. 4 is an exemplary plot of points between dJ and MP and the equationfor the best-fit line representing those points;

FIG. 5 is an exemplary plot of ranges of applicability for a model ofdrainage radii;

FIG. 6 is an exemplary plot of IPR for a slanted well;

FIG. 7 is an exemplary plot of IPR for a slanted well;

FIG. 8 is an exemplary plot of IPR for a slanted well;

FIG. 9 is an exemplary plot of IPR for a slanted well;

FIG. 10 is an exemplary plot of IPR for a slanted well;

FIG. 11 is an exemplary plot of IPR for a slanted well;

FIG. 12 is a flow chart depicting steps of a method employing the slantangle and/or a formation property to calculate a corrected drill angle;

FIG. 13A is a flow chart depicting the steps of a subroutine of a methodto determine the greater of two productivity indices to ultimatelycalculate a corrected drill angle;

FIG. 13B is a diagram of a snapshot of a drill head;

FIG. 14 is an exemplary diagram of the electronic connectivity of thedrill 1404 with a number of devices;

FIG. 15 is an exemplary diagram depicting the circuitry that can be in adrill guidance device;

FIG. 16 is an exemplary diagram depicting a programmable processor thatcan be employed in the drill guidance device; and

FIG. 17 is an exemplary diagram depicting the connectivity within aprocessor that can be employed in a drill guidance device.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Referring now to the drawings, wherein like reference numerals designateidentical or corresponding parts throughout the several views.

Aspects of the present disclosure are directed to a drill guidancedevice with circuitry that is configured to determine a slant angle of adrill based on directional sensor data collected from one or moresensors, determine one or more formation properties based on formationsensor data received from one or more sensors, and control an angle oftrajectory of a drill based on a corrected drill angle calculated basedon the slant angle and the formation properties. The drill guidancedevice can be electronically connected to a drill controller which cantransmit an electronic signal to control a drill by changing an angle oftrajectory of the drill. The sensors from which directional data andformation properties are collected can be located on the drill, but mayalso be at a distal location and electronically connected to the drillguidance device. The drill guidance device can be configured to work inconjunction with manual operation as well as autonomous operationwithout human intervention.

According to one implementation, the drill guidance device depends onseveral properties from which a corrected drill angle can be calculated.The drill guidance device may employ a measurement of a slant angle froma directional sensor including, but not limited to an accelerometer anda magnetometer. The drill guidance device may also employ a measurementof formation properties, such as formation permeability and formationthickness. In one implementation the formation permeability measurementis based on the formation sensor data received from a porosity sensor.In one implementation the formation thickness measurement is based on aformation sensor. In some implementations the formation sensor measuresdensity and chemical signatures of a rock formation to determine thetype of geological material at a drill site. In one implementation thedata obtained from the sensors is electronically transmitted to thecircuitry of the drill guidance device.

To determine the correct drill angle the device can use a function basedon the slant angle and formation properties. To derive this function, aseries of iterative procedures were executed to refine previouslyreported equations to derive one that can be used for drill guidance.

Accordingly, the model proposed here, referred to as a drill guidancemodel, can estimate PI or II of these two types of water wells commonlyused in the oil industry. Development of drill guidance model describedherein can be applied to slanted/highly-deviated water supplies andwater injection wells. The drill guidance model is based on simulationmodeling of several wells/reservoirs' scenarios that resulted inproposing a method for better estimation of the IPR of an isotropic andhomogenous reservoirs having water supply or water injectionslanted/highly-deviated wells. In deriving the drill guidance model,instead of calculating the pseudo-skin caused by the well slant,incremental PI/II is calculated and added to that of a vertical wellwith the same reservoir characteristics. Cinco model was used as thebasis in deriving the correlation. The drill guidance model proved itsreliability in predicting the IPR for several examples of data and wascompared to Cinco model.

In deriving the equations for the drill guidance model, the effect ofwell inclination can be formulated as a function of slant angle,reservoir thickness and average permeability. These three parameters canbe assembled together as a block to form a parameter denoted as (MP). Inone implementation, a trial-and-error approach can be used to determinea relationship between the MP and dJ that produces a drill guidancemodel that is able to predict the inflow performance for isotropic andhomogenous water reservoirs. The drill guidance model proved itsreliability in estimating IPR of slanted water-supplying andwater-injection wells in comparison to the Cinco model for a wide rangeof reservoir and well characteristics. The present disclosure isdirected to a device that employs the drill guidance model.

Rather than correcting the vertical IPR via the pseudo skin induced bythe slanted and highly-deviated well, an empirical correlation can begenerated based on a Cinco model to express deviation effect as anadditional productivity/injectivity as a function of one or morereservoir parameters. The empirical correlation, used interchangeablyherein with “the empirical model,” can be generated using results from asimulated base case, then conducting sensitivity analysis of severalreservoir parameters to create the drill guidance model which can becompared with the productivity index as predicted by the Cinco model.The empirical model refers to any model that is described herein fortesting. The empirical model which achieves the best correlation withthe Cinco model will be referred to as the drill guidance model.

Drilling a slanted and highly-deviated water supply and/or waterinjection wells through the pay zone can increase the reservoir exposedsurface area opened to flow, which can result in an increased IPR. Thisadditional flow reflects an additional productivity index (J) from thatof a vertical well:J _(slant) =J _(vertical) +dJ  (8)Where J_(slant) is i the Productivity/Injectivity Index for the slantedwater well (STB/DAY/PSI), J_(vertical) is the Productivity/InjectivityIndex for the vertical water well (STB/DAY/PSI), and dJ is the change inthe Productivity/Injectivity Index due to the slanted/highly-deviatednature of the water well (STB/DAY/PSI).

FIG. 1 is an example of the comparison of two well models to be drilledin a certain reservoir; a vertical well and a slanted well with an angleof 50° using Cinco correction pseudo skin factor. The graph illustratesthe increase in the productivity as measured by the empirical model,created when the well deviates with a predetermined angle. The empiricalmodel increases productivity (dJ) resulting from the well deviation, andto correlate the productivity with the slant angle value; in otherwords, to make (dJ) behave as a function of slant angle (θ).

In one implementation, assumptions can be made related to determiningproductivity for wells having slanted angles. For example, oneassumption is that the reservoir under study is isotropic and homogenousunder steady-state condition where the permeability in every direction(x, y, z) is equal and constant. The second assumption is that thereservoir is a water reservoir if the well is a water supply or an oilreservoir with water injector drilled in the aquifer area to support thereservoir pressure. The third assumption is that in all calculations,the viscosity used is 1 centipoise and the formation volume factor is 1bbl/STB, which are typical values for water injection wells. Thepreceding assumptions are not limiting and other assumptions can beemployed in some implementations.

In an example, the first step to create the drill guidance model is toset a base-case of a reservoir and well characteristics: 50 ft ofreservoir thickness, permeability of 25 md, 2000 ft of drainage radius,and reservoir pressure of 3000 psi. The difference between the verticalwell productivity index and the slanted well productivity index can becalculated for every well slant angle between 20° and 70°. Then, valuesof (dJ) are plotted against the angle, and the best-representing trendline is drawn through the points and its equation can be determinedusing non-linear regression technique, which is illustrated in FIG. 2.The model is:

$\begin{matrix}{{{dJ} = {{2e} - {5\;\theta^{2.373}}}}{{Therefore}\text{:}}} & (9) \\{J = {\frac{kh}{141.2{B\left\lbrack {\ln\left( \frac{r_{e}}{r_{w}} \right)} \right\rbrack}} + {2e} - {5\theta^{2.373}}}} & (10)\end{matrix}$As can be seen from equation (1), the parameters which affect theproductivity index for water supply and/or water injection wells inequation (1) can include slant angle (θ), permeability (k), thickness(h), drainage radius (r_(e)), and wellbore radius (r_(w)).

To check the validity and strength of this initial model, equation (1)was applied to predict the productivity index for different water wells'cases, and the results are presented in Table (1). The first testconducted on this model was to calculate (PI) and compare it with (PI)predicted by the Cinco model for the base case upon which the model wasinitially based. Case (1) in Table (1) shows that the initial modelgives an estimate for the productivity index. However, from cases (2)and (3) in Table (1) it is observed that (dJ), from equation (9), maynot be solely sensitive to slant angle. When equation (10) was used tocalculate (PI) for different permeability and thickness, the estimated(PI) indicated an inaccuracy in comparison to (PI) estimated by Cincomodel. So, permeability and thickness both have effects on (dJ), and canbe included in addition to slant angle in the drill guidance model.Viscosity, formation volume factor and wellbore radius are held constantfor water injection and/or water supply wells, and correlation may beunnecessary. Drainage radius shows very slight effect on the PI.

From this sensitivity analysis, the incremental productivity (dJ) causedby the well deviation can be a function of the slant angle (θ), theaverage permeability (k), and thickness of the reservoir (h). Thefunction can be written as:dJ=f(θ,k,h)  (11)

TABLE 1 Sensitivity analysis for model parameters Case 1 2 3 4 5 Slantangle 26° 42° 50° 63° 32° Permeability (md) 25 300 25 25 25 Thickness(ft) 50 50 150 50 50 Viscosity (cp) 1 1 1 6 1 Formation volume factor 11 1 1 1 (bbl/STB) Drainage radius (ft) 2000 2000 2000 2000 3500 Wellboreradius (ft) 0.3 0.3 0.3 0.3 0.3 PI by Cinco (bbl/day/psi) 1.06 13.913.94 0.24 1.02 PI by initial model (bbl/day/psi) 1.05 12.21 3.23 0.541.02

Equation (10) may be inaccurate when applied to various types ofreservoirs because it was a function of slant angle only. Then theparameters of permeability and thickness were included into the drillguidance model. But before that the data for the base case to build theempirical model, are presented in Table (2). In one implementation,permeability, thickness and angle are grouped together to form aparameter that can be called Model Parameter (MP). This (MP) is assumedto be:MP=hk sin(θ)  (12)

TABLE 2 Data for the base case Variable Value Unit External Boundaryr_(e) 2000 ft Radius Wellbore Radius r_(w) 0.3 ft Formation Volume B 1bbl/STB Factor Skin s 0 Viscosity μ 1 cp Slant Angle θ 20°, 30°, 40°,50°, 60°, 70° Average Permeability k 0.01, 0.1, 1, 4, 10, 35, 50, md 70,100, 250, 500, 700, 850, 1000 Pay Thickness h 10, 15, 30, 50, 75, 90,120, 250, ft 400, 500

The procedures for developing a model that is more accurate can besummarized as follows (1) for all combination of the variables presentin table (2), (J) is calculated using Darcy model including 6 selectedvalues of slant angle, 14 permeability values and 10 values for thethickness, which results in 840 cases, (2) for all combination (840case) of the variables present in table (2), (J) is calculated using theCinco model, (3) for each case from the combination of the variables,the difference between (J_(slanted)) and (J_(vertical)) is determined,(4) for all combination of variables, (MP) is calculated for each caseand then plotted against (dJ), which was determined in the previousstep, (5) By using a sort of nonlinear regression, an equation isdeveloped which relates (dJ) with (MP). FIG. 3 highlights the best-fitline. The equation of that best fit line is:dJ=0.0002MP ^(1.0486)  (13)And by substituting in equation (8) the model is described by thefollowing equations:

$\begin{matrix}{J = {\frac{kh}{141.2\left\lbrack {\ln\left( \frac{r_{e}}{r_{w}} \right)} \right\rbrack} + {0.0002{MP}^{1.0486}}}} & (14) \\{J = {\frac{kh}{141.2\left\lbrack {\ln\left( \frac{r_{e}}{r_{w}} \right)} \right\rbrack} + {0.0002\left( {{hk}\;{\sin(\theta)}} \right)^{1.0486}}}} & (15)\end{matrix}$Equation (15) incorporates the parameters of slant angle, thickness andpermeability and the parameters can be involved to calculate theadditional productivity, and eventually, the slanted well productivity.

In the next iteration, by using the trial-and-error approach, the term(MP) is changed and all the previous steps are repeated in order toimprove the model and minimize the error. A series of attempts andtrials were conducted to improve the accuracy of the model and theresults are recorded in Table (3).

As a result of the analysis, the empirical model with the highestcoefficient of determination, as appearing in FIG. 4, was chosen to makeapproximate calculations of productivity/injectivity in this study.Hence, the full form of the drill guidance model that can be employed topredict the productivity index for slanted and highly-deviated waterwell can be written as:

$\begin{matrix}{J = {\frac{kh}{141.2\left\lbrack {\ln\left( \frac{r_{e}}{r_{w}} \right)} \right\rbrack} + {0.0025\left\lbrack {h^{0.65}{k^{0.52}\left( {\tan\;\frac{\theta}{4}} \right)}^{1.22}} \right\rbrack}^{1.9267}}} & (16)\end{matrix}$Equation (16), which is the drill guidance model, can be represented ina way that productivity/injectivity of a deviated water well equals theproductivity/injectivity of a vertical water well with an equivalentthickness. This equivalent thickness can be derived from equation (16)as:

$\begin{matrix}{h_{equivalent} = {h + {{\frac{0.353}{k}\left\lbrack {\ln\left( \frac{r_{e}}{r_{w}} \right)} \right\rbrack}\left\lbrack {h^{0.65}{k^{0.52}\left( {\tan\;\frac{\theta}{4}} \right)}^{1.22}} \right\rbrack}^{1.9267}}} & (17)\end{matrix}$For example, a water well with an angle of 35° drilled through areservoir having a permeability of 80 md, thickness of 120 ft, externalradius of 1500 ft and 3500 psi pressure is going to have aproductivity/injectivity index of:

$J = {{\frac{80 \times 120}{141.2\left\lbrack {\ln\left( \frac{1500}{0.3} \right)} \right\rbrack} + {0.0025\left\lbrack {120^{0.65} \times 80^{0.52}\left( {\tan\;\frac{35}{4}} \right)^{1.22}} \right\rbrack}^{1.9267}} = {8.98\mspace{14mu}{bbl}\text{/}{day}\text{/}{psi}}}$Using Cinco model, PI will be:J=9.01 bbl/day/psiUsing equation (17) to calculate thickness of the reservoir that wouldhave the same productivity of 8.98 bbl/day/psi:

$h_{equivalent} = {{120 + {{\frac{0.353}{80}\left\lbrack {\ln\left( \frac{1500}{0.3} \right)} \right\rbrack}\left\lbrack {120^{0.65} \times 80^{0.52}\left( {\tan\;\frac{35}{4}} \right)^{1.22}} \right\rbrack}^{1.9267}} = {135\mspace{14mu}{ft}}}$The productivity/injectivity of a vertical water well penetrating areservoir having a thickness of 135 ft is:

$J = {\frac{80 \times 135}{141.2\left\lbrack {\ln\left( \frac{1500}{0.3} \right)} \right\rbrack} = {8.98\mspace{14mu}{bbl}\text{/}{day}\text{/}{psi}}}$When it comes to the injector wells, equation (16) can be used topredict their injectivity index if they inject water. Similarly, thedrill guidance model in this case may estimate the additionalinjectivity, caused when the well penetrates the reservoirdirectionally, and add the additional injectivity to the injectivity ofa vertical well.

TABLE 3 Model Development Through Several Trials Generated Equation fromNonlinear Coefficient of Assumed Form for (MP) Regression Determination(R²) MP = hksin(θ) dJ = 0.0002MP^(1.0486) 0.9635 MP = {square root over(h k)} sin(θ) dJ = 0.0003MP^(2.0934) 0.9862 MP = {square root over (hk)} [sin(θ)]² dJ = 0.0009MP^(1.9855) 0.9819 MP = {square root over (h ksin(θ))} dJ = 0.0002MP^(2.0973) 0.9635 MP = {square root over (h k)}[sin(θ)]^(1.5) dJ = 0.0005MP^(2.054) 0.9918 MP = h^(0.8)k^(0.7)[sin(θ)]²dJ = 0.0002MP^(1.4517) 0.997  MP = h^(0.9)k^(0.7)[sin(θ)]² dJ =0.0001MP^(1.426) 0.9981 MP = h^(0.6) {square root over (k)}[sin(θ)]² dJ= 0.0002MP^(2.0118) 0.9978 MP = h^(0.65)k^(0.52)[sin(θ)]^(1.52) dJ =0.0002MP^(1.9259) 0.9982${MP} = {h^{0.65}{k^{0.52}\left\lbrack {\sin\left( \frac{\theta}{2} \right)} \right\rbrack}^{1.4}}$dJ = 0.0008MP^(1.9163) 0.999 ${MP} = {h^{0.67}{k^{0.52}\left\lbrack {\sin\left( \frac{\theta}{2} \right)} \right\rbrack}^{1.4}}$dJ = 0.0007MP^(1.9066) 0.999 ${MP} = {h^{0.6}{k^{0.4}\left\lbrack {\sin\left( \frac{\theta}{3} \right)} \right\rbrack}^{1.4}}$dJ = 0.0034MP^(2.3261) 0.9866${MP} = {h^{0.65}{k^{0.5}\left\lbrack {\sin\left( \frac{\theta}{3} \right)} \right\rbrack}^{1.25}}$dJ = 0.0013MP^(1.9873) 0.9993${MP} = {h^{0.65}{k^{0.5}\left\lbrack {\sin\left( \frac{\theta}{4} \right)} \right\rbrack}^{1.2}}$dJ = 0.0024MP^(1.9917) 0.9993${MP} = {h^{0.65}{k^{0.5}\left\lbrack {\sin\left( \frac{\theta}{5} \right)} \right\rbrack}^{1.2}}$dJ = 0.0041MP^(1.9912) 0.9993${MP} = {h^{0.65}{k^{0.5}\left\lbrack {\tan\left( \frac{\theta}{3} \right)} \right\rbrack}^{1.25}}$dJ = 0.0013MP^(1.9783) 0.9992${MP} = {h^{0.65}{k^{0.52}\left\lbrack {\tan\left( \frac{\theta}{4} \right)} \right\rbrack}^{1.2}}$dJ = 0.0023MP^(1.9289) 0.9995${MP} = {h^{0.65}{k^{0.52}\left\lbrack {\tan\left( \frac{\theta}{4} \right)} \right\rbrack}^{1.22}}$dJ = 0.0025MP^(1.9267) 0.9996Equation (16) can predict the productivity/injectivity for slanted andhighly-deviated water wells in a way that is comparable to Cinco model.The drill guidance model may produce reliable estimates for thefollowing ranges of reservoir and well conditions including paythickness from 10 ft to 800 ft, permeability from 0.01 to 1000 md, andzero skin.

In one implementation, the drill guidance model can be applicable withsome constraints related to the drainage radius. For example, the drillguidance model may predict the productivity/injectivity for a deviatedwell by an angle between 20° to 70° when the drainage radius is greaterthan 1500 ft.

In another implementation, the reservoirs with smaller external radiusthe range of slant angles on which the drill guidance model can beapplicable decreases. For example, when the drainage radius is 500 ft,the drill guidance model can give approximate predictions ofproductivity for slant angles between 20° and 50°. FIG. 5 illustratesthese observations for the drill guidance model's applicable range ofslant angles in relation to drainage radii.

FIGS. 6-8 represent examples for using the model to estimate PI fordifferent reservoir conditions and well geometries within examples ofranges, whereas FIGS. 9-11 are examples of cases which apply the drillguidance model outside of the example ranges of FIGS. 6-8, whichresulted in results of lower accuracy than the results of FIGS. 6-8.

TABLE 4 Nomenclature J Productivity Index θ Slant Angle s Skin Factors_(θ) Slanted Skin h Formation Thickness k Absolute FormationPermeability k_(h) Horizontal Permeability k_(v) Vertical Permeabilityk_(x) Permeability in x Direction k_(y) Permeability in y Direction μViscosity q Flow Rate B Formation Volume Factor P_(e) External BoundaryPressure P_(wf) Bottomhole Flowing Pressure r_(e) External BoundaryRadius r_(w) Wellbore Radius L Well Length

In one implementation the circuitry of the drill guidance device isconfigured to calculate a corrected drill angle by employing ameasurement of the slant angle, formation permeability and formationthickness. The slant angle, the formation permeability, and theformation thickness can be used to determine a PI. The greater value ofa first and second PI value, each calculated from at least one differentvalue of slant angle, formation permeability, and formation thickness,determines the corrected drill angle. The circuitry can be configured toemploy equation (16), from the derivation provided herein, in thecalculation.

Equation (16) also uses terms r_(e) and r_(w), which are values of thedrainage radius or external boundary radius of a well site and awellbore radius, which can be pre-set into the equation and aredependent on the drilling site. The preset values for r_(e) may bebetween 500 ft and 5000 ft, between 600 ft and 4500 ft, between 700 ftand 4000 ft, between 800 ft and 3750 ft, between 900 ft and 3500 ft,between 100 ft and 3250 ft, between 1100 ft and 3000 ft, between 1200 ftand 2750 ft, between 1300 ft and 2500 ft, between 1400 ft and 2250 ft,between 1500 ft and 2000 ft, between 1600 ft and 1750 ft. The presetvalues for r_(w) may be between 0.01 ft and 1 ft, between 0.05 ft and0.9 ft, between 0.1 ft and 0.8 ft, between 0.15 ft and 0.7 ft, between0.2 ft and 0.6 ft, between 0.25 ft and 0.5 ft, between 0.3 ft and 0.4ft. The circuitry is not limited to employing the above equation and canbe configured to employ a plurality of equations. In one implementationthe circuitry of the drill guidance device is also configured torecursively calculate the PI as sensor data is received to continuallycalculate a corrected drill angle. In one implementation the recursivecalculation allows an autonomously controlled drill to be continuallycorrected in its angle of trajectory such that the PI is maximized. Todetermine a maximum PI, the PI can be at least 20% greater than theprevious value, at least 18% greater than the previous value, at least15% greater than the previous value, at least 12% greater than theprevious value, at least 10% greater than the previous value, at least8% greater than the previous value, at least 5% greater than theprevious value, at least 2% greater than the previous value, at least 1%greater than the previous value, or any other predetermined percentagegreater than the previous percentage.

According to another aspect, a method to control a trajectory of a drillwhich can determine a slant angle of a drill based on directional sensordata received from one or more sensor devices, determining one or moreformation properties based on formation sensor data received from theone or more sensor devices, and controlling an angle of trajectory ofthe drill based on a corrected drill angle calculated based on the slantangle and the formation properties.

The formation properties can include, but are not limited to formationpermeability and formation thickness. The slant angle, formationpermeability, and formation thickness can be used to calculate a PI. Thegreater of two PI values, each of which are a function of at least onedifferent value for slant angle, formation permeability, and formationthickness, determines the corrected drill angle to control thetrajectory of a drill.

FIG. 12, FIG. 13A, and FIGS. 14-15 are exemplary flowcharts of processesfor controlling a trajectory of a drill. The method to control atrajectory of a drill can be implemented several ways. Twoimplementations are described herein as examples, and are not intendedto be limiting descriptions. One implementation can be a measuring whiledrilling (MWD) method meaning that while drilling is in progress themethod can correct the drill trajectory. Implementation as an MWD may beaccomplished by providing the corrected drill angle in a signal to adrill controller and the drill controller can determine the appropriateresponse to the signal based on a preset threshold to determine whetherit is necessary to change the drill trajectory by the corrected angle.The preset threshold may be more than 20% difference between the currentdrill trajectory and the corrected drill trajectory, more than 15%difference between the current drill trajectory and the corrected drilltrajectory, more than 10% difference between the current drilltrajectory and the corrected drill trajectory, more than 5% differencebetween the current drill trajectory and the corrected drill trajectory,more than 3% difference between the current drill trajectory and thecorrected drill trajectory, more than 1% difference between the currentdrill trajectory and the corrected drill trajectory, or any otherpredetermined percentage greater than the previous percentage. Thesecond implementation may be a predictive method in which the trajectoryof the drill is determined prior to drilling.

The corrected drill angle is calculated based on a PI, which can becalculated as a function of the slant angle (θ), the formationpermeability (k), and the formation thickness (h). The slant angle (θ),the formation permeability (k), and the formation thickness (h) aremeasurements that can be determined from measurements by the sensor ormanually entered values. The corrected drill angle is determined by avariance in two productivity indices: one PI is calculated on ameasurement at a time point and a second PI is calculated on ameasurement at a later time point such that (θ), (k), or (h) havechanged. If the second PI is greater than the first PI then thecorrected drill angle is determined by the difference in the slant anglebetween the two PI calculations. The corrected drill angle is thentransmitted to the drill controller. This process can be performedrecursively to continually provide the corrected drill angle based on apositive difference between the second PI and the first PI. A positivedifference, as used herein, is the result of a second PI greater thanthe first PI.

In an implementation of the method, the corrected drill angle isdetermined by a difference between two productivity indices: one PI iscalculated on a measurement made by sensors or other geologic data and asecond PI is calculated based on an incremented value of any combinationof (θ), (k), or (h) or permutation of (θ), (k), or (h). The correcteddrill angle is determined by the difference in the slant angle betweenthe two PI calculations. This process can be recursive to continuallyprovide the corrected drill angle based on a positive difference betweenthe second PI and the first PI. In some implementations of this methodthe productivity indices of subsequent incremental calculations can beplotted graphically to find the greatest positive difference between twoproductivity indices. FIGS. 12-15 depict exemplary flow charts showingvariations of the calculation of the corrected drill angle.

FIG. 12 depicts a flow chart of a general method 1200 to calculate thecorrected drill angle for a predictive method. The first step 1202 is toreceive sensor data which can be from mechanical sensors integral to adrill head or connected wirelessly. The sensors data can be received viaa wireless connection to a computer which can then process the data.

The next step 1204 is to determine the current values of a slant angleand/or a formation property. The determining requires a calculation of avalue for the slant angle and the formation property from the datagathered from the sensors. The determining may also include looking upthe values in a database. The values can be assigned to variables (θ),(k), or (h), or any combination of the variables.

The next step 1206 is to determine which variable to increment. Theincremented variable can be determined by a human user or a presetalgorithm that may use variables (θ), (k), or (h), or any combination ofthe variables to be incremented. The variables may be incremented by atleast 0.5% of its value, at least 1% of its value, at least 3% of itsvalue, at least 5% of its value, at least 10% of its value, at least 15%of its value. In one implementation the variables may be incrementedbased on historical data obtained from a the database which stores dataon comparable reservoir locations.

The next step 1208 is the determination of the PI. The PI is dependenton variables (θ), (k), or (h), or any combination of the variables ofthe previous steps 1204 and 1206. Step 1208 is a subroutine that isdepicted in FIG. 13. Step 1208 can include a recursive step until amaximum PI is determined.

The subroutine of step 1208 is depicted in FIG. 13A. The input to thefirst step 1302 of FIG. 13 is to determine a first PI which is afunction of the initially determined slant angle and/or formationproperties as in step 1204. The second step 1304 is to determine thesecond PI which can use the values of the variables determined by step1206. In one implementation equation (16) is the function used todetermine the PI in steps 1302 and 1304. Step 1304 may also make adetermination of a second PI from sensor data which has changed overtime during the drilling process (See FIG. 13B). For example a drill maychange the slant angle or the geological formation through which thedrill is moving may be composed of a different material, therefore thevariables (θ), (k), or (h) may be different. In FIG. 13B an exemplarydepiction of a drill 1315 in a slanted well is shown. The slant angle,represented by (θ), can be measured from an axis 1316. The drill movesfrom one section of a first formation 1317, resulting in a slant angle(θ₁), formation permeability (k₁), and formation thickness (h₁), at aninitial time (t₀), then moving into a second formation 1318 resulting ina slant angle (θ₂), formation permeability (k₂), and formation thickness(h₂), at a later time (t₁). As an example, referring to FIG. 13B, in aMWD implementation of the method to determine a corrected angle oftrajectory, the first PI in step 1302 can use (θ₁), (k₁), (h₁) of t₀ andthe second PI in step 1304 can use (θ₂), (k₂), (h₂) of t₁.

Referring again to FIG. 13A, step 1306 is a decision step to determineif the second PI is greater than the first PI. This step is based on theunderstanding that a bigger value for the PI correlates to the improvedproductivity of the oil well. If the decision is “YES” then the maximumPI value is determined to be the second PI value (1308) and the secondPI value is the output of the subroutine to be input into step 1210 ofFIG. 12. If the decision is “NO” then next step 1310 is to update thevariables and return to the beginning of the subroutine at step 1302.This is a recursive implementation of the subroutine, but the subroutinemay also be implemented as a non-recursive calculation.

Referring again to FIG. 12, the step 1210 is to decide if the PIdetermined from the subroutine of 1208 is the maximum of a comparison.If the decision is “YES” the next step 1212 is to change the settings ofthe variables for the corrected drill angle and/or send a control signalwith the corrected drill angle. If the decision from step 1210 is “NO”then the next step 1211 is to maintain the current settings for thevariables and thus not changing the angle of trajectory of the drill.

FIG. 14 is an exemplary illustration of a drill guidance device system1400, according to certain implementations. The computer 1410 representsat least one computer 1410 and can act as a drill controller that isconnected to a server 1406, which can also be the drill guidance device,a drill 1404, a database 1408, and a mobile device 1412, via a network1402. In some implementations, the computer 1410 is used to view datacollected over various drill guidance implementations. In addition, thecomputer 1410 can be used by a person to monitor the drill guidancedevice 1406 and the drill 1404, current drill guidance data, theformation sensors, or the slant angle data of the drill 1404 via aninterface at the computer 1410.

The server 1406 represents one or more drill guidance devices connectedto the computer 1410, the database 1408, and the mobile device 1412 viathe network 1402. In some implementations, processing circuitry of theserver 1406 receives instructions from the mobile device 1412 based onsensor data obtained by one or more sensors on the drill 1404 connectedto the mobile device 1412. Note that each of the functions of thedescribed implementations may be implemented by one or more processingcircuits. A processing circuit includes a programmed processor (forexample, processor 1600 of FIG. 16), as a processor includes circuitry.A processing circuit/circuitry may also include devices such as anapplication specific integrated circuit (ASIC) and conventional circuitcomponents arranged to perform the recited functions. The processingcircuitry can be referred to interchangeably as circuitry throughout thedisclosure.

The database 1408 represents one or more databases connected to thecomputer 1410, the server 1406, and the mobile device 1412 via thenetwork 1402. In some implementations, the drill guidance data is storedin the database 1408. For example, the drill guidance data from current,concurrent, or previous guidance implementations can be stored by theprocessing circuitry of the drill guidance device 1406 to provide datamodels that can be used to assist in the predictive method for drillguidance. In MWD implementations, the database 1408 can be used togather the current data and to provide comparative data from previouslystored data.

The mobile device 1412 represents one or more mobile devices connectedto the computer 1410, the server 1406, and the database 1408 via thenetwork 1402. The network 1402 represents one or more networks, such asthe Internet, connecting the computer 1410, the drill 1404, the drillguidance device 1406, the database 1408, and the mobile device 1412. Thenetwork 1402 can also communicate via wireless networks such as WI-FI,BLUETOOTH, cellular networks including EDGE, 3G and 4G wireless cellularsystems, or any other wireless form of communication that is known.

As would be understood by one of ordinary skill in the art, based on theteachings herein, the mobile device 1412 or any other external devicecould also be used in the same manner as the computer 1410 to monitorthe slant angle and formation properties that the drill trajectory. Inaddition, the computer 1410 and mobile device 1412 can be referred tointerchangeably throughout the disclosure. Details regarding theprocesses performed by drill guidance system 1400 are discussed furtherherein. In addition, one or more sensors can be connected to the mobiledevice 1412, such as a magnetometer or porosity sensor, resistivitysensors or conductivity sensors, and any other type of formation sensor.The formation sensors can be integral to the drill guidance device orcan be connected to the drill guidance device via a wired or wirelessconnection. The sensors can be integral to the drill 1404 or can beconnected to the drill via wired or wireless connection.

FIG. 15 depicts an exemplary diagram of the circuitry employed in thedrill guidance device and a hardware description of the circuitryaccording to exemplary implementations is described with reference toit. In FIG. 15, circuitry of the drill guidance device includes a CPU1500 which performs the processes described above/below. The processdata and instructions may be stored in memory 1502. These processes andinstructions may also be stored on a storage medium disk 1504 such as ahard drive (HDD) or portable storage medium or may be stored remotely.Further, the claimed advancements are not limited by the form of thecomputer-readable media on which the instructions of the inventiveprocess are stored. For example, the instructions may be stored on CDs,DVDs, in FLASH memory, RAM, ROM, PROM, EPROM, EEPROM, hard disk or anyother information processing device with which the circuitry of thedrill guidance device communicates, such as a server or computer.

Further, the claimed advancements may be provided as a utilityapplication, background daemon, or component of an operating system, orcombination thereof, executing in conjunction with CPU 1500 and anoperating system such as Microsoft Windows 7, UNIX, Solaris, LINUX,Apple MAC-OS and other systems known to those skilled in the art.

The hardware elements in order to achieve the circuitry of the drillguidance device may be realized by various circuitry elements, known tothose skilled in the art. For example, CPU 1500 may be a Xenon or Coreprocessor from Intel of America or an Opteron processor from AMD ofAmerica, or may be other processor types that would be recognized by oneof ordinary skill in the art. Alternatively, the CPU 1500 may beimplemented on an FPGA, ASIC, PLD or using discrete logic circuits, asone of ordinary skill in the art would recognize. Further, CPU 1500 maybe implemented as multiple processors cooperatively working in parallelto perform the instructions of the inventive processes described above.

The circuitry of the drill guidance device in FIG. 15 also includes anetwork controller 1506, such as an Intel Ethernet PRO network interfacecard from Intel Corporation of America, for interfacing with network1402. As can be appreciated, the network 1402 can be a public network,such as the Internet, or a private network such as an LAN or WANnetwork, or any combination thereof and can also include PSTN or ISDNsub-networks. The network 1402 can also be wired, such as an Ethernetnetwork, or can be wireless such as a cellular network including EDGE,3G and 4G wireless cellular systems. The wireless network can also beWiFi, Bluetooth, or any other wireless form of communication that isknown.

The circuitry of the drill guidance device further includes a displaycontroller 1508, such as a NVIDIA GeForce GTX or Quadro graphics adaptorfrom NVIDIA Corporation of America for interfacing with display 1510,such as a Hewlett Packard HPL2445w LCD monitor. A general purpose I/Ointerface 1512 interfaces with a keyboard and/or mouse 1514 as well as atouch screen panel 1516 on or separate from display 1510. Generalpurpose I/O interface also connects to a variety of peripherals 1516including printers and scanners, such as an OfficeJet or DeskJet fromHewlett Packard.

A sound controller 1507 is also provided in the circuitry of the drillguidance device, such as Sound Blaster X-Fi Titanium from Creative, tointerface with speakers/microphone 1522 thereby providing sounds and/ormusic.

The general purpose storage controller 1524 connects the storage mediumdisk 1504 with communication bus 1526, which may be an ISA, EISA, VESA,PCI, or similar, for interconnecting all of the components of thecircuitry of the drill guidance device. A description of the generalfeatures and functionality of the display 1510, keyboard and/or mouse1514, as well as the display controller 1508, storage controller 1524,network controller 1506, sound controller 1507, and general purpose I/Ointerface 1512 is omitted herein for brevity as these features areknown.

The exemplary circuit elements described in the context of the presentdisclosure may be replaced with other elements and structureddifferently than the examples provided herein. Moreover, circuitryconfigured to perform features described herein may be implemented inmultiple circuit units (e.g., chips), or the features may be combined incircuitry on a single chipset, as shown on FIG. 16.

FIG. 16 shows a schematic diagram of a data processing system, accordingto certain implementations, for performing a method to control atrajectory of a drill. The data processing system is an example of acomputer in which code or instructions implementing the processes of theillustrative implementations may be located.

In FIG. 16, data processing system 1600 employs a hub architectureincluding a north bridge and memory controller hub (NB/MCH) 1625 and asouth bridge and input/output (I/O) controller hub (SB/ICH) 1620. Thecentral processing unit (CPU) 1630 is connected to NB/MCH 1625. TheNB/MCH 1625 also connects to the memory 1645 via a memory bus, andconnects to the graphics processor 1650 via an accelerated graphics port(AGP). The NB/MCH 1625 also connects to the SB/ICH 1620 via an internalbus (e.g., a unified media interface or a direct media interface). TheCPU Processing unit 1630 may contain one or more processors and even maybe implemented using one or more heterogeneous processor systems.

For example, FIG. 17 shows one implementation of CPU 1630. In oneimplementation, the instruction register 1738 retrieves instructionsfrom the fast memory 1740. At least part of these instructions arefetched from the instruction register 1738 by the control logic 1736 andinterpreted according to the instruction set architecture of the CPU1730. Part of the instructions can also be directed to the register1732. In one implementation the instructions are decoded according to ahardwired method, and in another implementation the instructions aredecoded according a microprogram that translates instructions into setsof CPU configuration signals that are applied sequentially over multipleclock pulses. After fetching and decoding the instructions, theinstructions are executed using the arithmetic logic unit (ALU) 1734that loads values from the register 1732 and performs logical andmathematical operations on the loaded values according to theinstructions. The results from these operations can be feedback into theregister and/or stored in the fast memory 1740. According to certainimplementations, the instruction set architecture of the CPU 1630 canuse a reduced instruction set architecture, a complex instruction setarchitecture, a vector processor architecture, a very large instructionword architecture. Furthermore, the CPU 1630 can be based on the VonNeuman model or the Harvard model. The CPU 1630 can be a digital signalprocessor, an FPGA, an ASIC, a PLA, a PLD, or a CPLD. Further, the CPU1630 can be an x86 processor by Intel or by AMD; an ARM processor, aPower architecture processor by, e.g., IBM; a SPARC architectureprocessor by Sun Microsystems or by Oracle; or other known CPUarchitecture.

Referring again to FIG. 16, the data processing system 1600 can includethat the SB/ICH 1620 is coupled through a system bus to an I/O Bus, aread only memory (ROM) 1656, universal serial bus (USB) port 1664, aflash binary input/output system (BIOS) 1668, and a graphics controller1658. PCI/PCIe devices can also be coupled to SB/ICH 1620 through a PCIbus 1662.

The PCI devices may include, for example, Ethernet adapters, add-incards, and PC cards for notebook computers. The Hard disk drive 1660 andCD-ROM 1666 can use, for example, an integrated drive electronics (IDE)or serial advanced technology attachment (SATA) interface. In oneimplementation the I/O bus can include a super I/O (SIO) device.

Further, the hard disk drive (HDD) 1660 and optical drive 1666 can alsobe coupled to the SB/ICH 1620 through a system bus. In oneimplementation, a keyboard 1670, a mouse 1672, a parallel port 1678, anda serial port 1676 can be connected to the system bust through the I/Obus. Other peripherals and devices that can be connected to the SB/ICH1620 using a mass storage controller such as SATA or PATA, an Ethernetport, an ISA bus, a LPC bridge, SMBus, a DMA controller, and an AudioCodec.

Moreover, the present disclosure is not limited to the specific circuitelements described herein, nor is the present disclosure limited to thespecific sizing and classification of these elements. For example, theskilled artisan will appreciate that the circuitry described herein maybe adapted based on changes on battery sizing and chemistry, or based onthe requirements of the intended back-up load to be powered.

The above-described hardware description is a non-limiting example ofcorresponding structure for performing the functionality describedherein.

FIGS. 12-13A illustrate exemplary algorithmic flowchart for performing amethod to control a trajectory of a drill according to one aspect of thepresent disclosure. The hardware description above, exemplified by anyone of the structure examples shown in FIG. 14, 15, or 17, constitutesor includes specialized corresponding structure that is programmed orconfigured to perform the algorithm shown in FIGS. 12-13A. For example,the algorithm shown in FIG. 12 may be completely performed by thecircuitry included in the single device shown in FIG. 14 or the chipsetas shown in FIG. 15, or the algorithm may be completely performed in ashared manner distributed over the circuitry of any plurality of thedevices shown in FIG. 17.

The method described herein and exemplified in FIGS. 12-13A can beimplemented by a non-transitory computer readable medium.

Obviously, numerous modifications and variations are possible in lightof the above teachings. It is therefore to be understood that within thescope of the appended claims, the invention may be practiced otherwisethan as specifically described herein.

Thus, the foregoing discussion discloses and describes merely exemplaryembodiments of the present invention. As will be understood by thoseskilled in the art, the present invention may be embodied in otherspecific forms without departing from the spirit or essentialcharacteristics thereof. Accordingly, the disclosure of the presentinvention is intended to be illustrative, but not limiting of the scopeof the invention, as well as other claims. The disclosure, including anyreadily discernible variants of the teachings herein, define, in part,the scope of the foregoing claim terminology such that no inventivesubject matter is dedicated to the public.

The invention claimed is:
 1. A drill guidance device comprising: circuitry configured to: determine a slant angle of a drill based on directional sensor data received from one or more sensor devices, determine one or more formation properties based on formation sensor data received from the one or more sensor devices, determine at least one of the slant angle or the formation property to increment, determine a first productivity index from the slant angle or the formation property, determine a second productivity index from an incremented slant angle or an incremented formation property, and calculate a corrected drill angle based on the slant angle and the formation properties corresponding to the greater of the first productivity index and the second productivity index and output the corrected drill angle to a drill controller configured to control an angle of trajectory of the drills wherein the first productivity index and the second productivity index (J) is defined by: ${J = {\frac{kh}{141.2\left\lbrack {\ln\left( \frac{r_{e}}{r_{w}} \right)} \right\rbrack} + {0.0025\left\lbrack {h^{0.65}{k^{0.52}\left( {\tan\;\frac{\theta}{4}} \right)}^{1.22}} \right\rbrack}^{1.9267}}},$ wherein r

is a drainage radius or an external boundary radius and /+ is a wellbore radius, slant angle is 0, formation permeability is k, and formation thickness is h.
 2. The drill guidance device of claim 1, wherein the circuitry is further configured to determine the slant angle based on the directional sensor data received from at least one of an accelerometer and a magnetometer.
 3. The drill guidance device of claim 1, wherein one of the formation properties is a formation permeability.
 4. The drill guidance device of claim 3, wherein the formation permeability is based on the formation sensor data received from a porosity sensor.
 5. The drill guidance device of claim 1, wherein one of the formation properties is a formation thickness.
 6. The drill guidance device of claim 5, wherein the formation thickness is based on the formation sensor data received from a resistivity sensor or a conductivity sensor.
 7. The drill guidance device of claim 1, wherein the circuitry is further configured for manual guidance of the drill.
 8. The drill guidance device of claim 1, wherein the circuitry is further configured to recursively calculate the second productivity index when the second productivity index is less than the first productivity index.
 9. The drill guidance device of claim 1, wherein the circuitry is further configured to determine the corrected drill angle based on a productivity index predictively calculated by accessing historical data from memory.
 10. The drill guidance device of claim 1, wherein the corrected drill angle is based on a continuously calculated productivity index in a measuring while drilling operation.
 11. A method to control a trajectory of a drill, comprising: determining a slant angle of a drill based on directional sensor data received from one or more sensor devices; determining one or more formation properties based on formation sensor data received from the one or more sensor devices; calculating a corrected drill angle based on the slant angle and the formation properties; and outputting the corrected drill angle to a drill controller configured to control an angle of trajectory of the drill, wherein the corrected drill angle is based on a productivity index (J) calculated as a function of the slant angle and at least one of a formation permeability and a formation thickness, and wherein the productivity index (J) is calculated based on the function: ${J = {\frac{kh}{141.2\left\lbrack {\ln\left( \frac{r_{e}}{r_{w}} \right)} \right\rbrack} + {0.0025\left\lbrack {h^{0.65}{k^{0.52}\left( {\tan\;\frac{\theta}{4}} \right)}^{1.22}} \right\rbrack}^{1.9267}}},$ wherein r_(e) is a drainage radius or an external boundary radius and r_(w) is a wellbore radius slant angle is θ, formation permeability is k, and formation thickness is h.
 12. The method of claim 11, wherein the productivity index is recursively calculated.
 13. The method of claim 11, wherein calculating the corrected drill angle further comprises incrementing at least one of the slant angle or the formation properties to form an incremented slant angle or an incremented formation property.
 14. The method of claim 13, further comprising calculating a first productivity index with the slant angle or the formation property and a second productivity index with the incremented slant angle or the incremented formation property and determining when the second productivity index is greater than the first productivity index.
 15. The method of claim 14, further comprising determining the corrected drill angle associated with the incremented formation property or the incremented slant angle when the second productivity index is greater than the first productivity index. 